Computation of Critical Exponent ηat O(1/N^3) in the Four Fermi Model in Arbitrary Dimensions

TL;DR

This paper advances the conformal bootstrap program by computing the fermion anomalous dimension $\eta$ at $O(1/N^3)$ for the $O(N)$ Gross-Neveu model in arbitrary dimensions. It develops a fermionic conformal-triangle bootstrap framework, derives a master equation that isolates $\eta_3$, and evaluates massless four-fermion graphs with regulator parameters to obtain the result. The main analytic expression for $\eta_3$ is given in terms of $\mu=d/2$ and special functions, with a concrete $d=3$ value that involves $\zeta(3)$ and $\ln 2$, illustrating the structure found in the bosonic counterpart. The work demonstrates the applicability of conformal methods to fermionic theories and suggests extensions to gauge theories like QED, enabling deeper probes of conformal dynamics in high-dimensional settings.

Abstract

We solve the conformal bootstrap equations of the four fermi model or $O(N)$ Gross Neveu model to deduce the fermion anomalous dimension of the theory at $O(1/N^3)$ in arbitrary dimensions.